The present invention pertains to nuclear magnetic resonance (NMR) spectroscopy, and in particular to NMR apparatus for and methods of improving the quality of an NMR spectrum.
The nuclei of many atoms possess non-zero angular momentum or spin. Where the nuclei have a net charge, the spin produces a magnetic moment. When a sample containing such nuclei is placed in a constant external magnetic field (e.g., B0 in the z-direction), the net magnetic moments of the nuclei attempt to line up with the magnetic field. Some nuclei align themselves parallel to the magnetic field (i.e., in the positive z-direction), while others align themselves antiparallel to the magnetic field (i.e., in the negative z-direction). These two different orientations (xe2x80x9cstatesxe2x80x9d) of the nuclei have different energies, with the population difference being inversely related to the energy difference between the two states.
At equilibrium, more nuclei will be in the low-energy state than in the high-energy state. The individual magnetic moments, however, cannot perfectly line up with the external magnetic field, but rather are tilted at an angle and thus precess at an angle about the imposed magnetic field axis at a particular frequency, known as the Larmor frequency.
If an oscillating external magnetic field (typically, pulses of electromagnetic energy in the radio frequency (xe2x80x9crfxe2x80x9d) range) is applied to the nuclei at the Larmor frequency, a resonance occurs, whereby the rf energy is absorbed due to the excess spin population of nuclei in the low energy state. This causes the magnetic moments in the lower energy state to flip to the higher energy state. Depending on the duration of the rf pulse, the populations of the two energy states will be perturbed from the equilibrium populations. When the oscillating magnetic field ceases, the precession of magnetic moments generates an electromagnetic signal that can be detected by a receiver coil appropriately arranged relative to the sample. The receiver coil converts the received signal into an electrical signal, which can then be analyzed. The populations of parallel and antiparallel nuclei return to an equilibrium state with a characteristic time period T1, known as the nuclear spin-lattice or longitudinal relaxation time.
Different nuclei precess at different frequencies. Accordingly, at a particular magnetic field strength, the nuclei will generally absorb energy at certain characteristic radio frequencies. Also, nuclei of the same nuclear species will absorb energy at shifted frequencies, depending upon their molecular environment. This shift, called the xe2x80x9cchemical shift,xe2x80x9d is characteristic of an atom""s position in a given molecule. Plots of chemical shift (typically measured in parts-per-million or xe2x80x9cppmxe2x80x9d) vs. signal strength (e.g., mV) reveal the energy absorption peaks (xe2x80x9cresonancesxe2x80x9d) of the nuclei and provide a chemical analysis or xe2x80x9cspectrumxe2x80x9d of a given sample subject to NMR. In particular, NMR spectroscopy is used to characterize the structure and dynamics of proteins, nucleic acids, carbohydrates and their complexes, much in the way crystallography is used. NMR is also used in vivo to monitor and characterize living tissue, and in particular has been used to monitor defects in energy metabolism in animals. Details about NMR, including NMR spectroscopy, can be found in the book by S. Webb, The Physics of Medical Imaging, Institute of Physics Publishing, Ltd., 1992, Chapter 8.
A technique used in NMR to acquire a signal from the sample being measured is called the xe2x80x9cspin echoxe2x80x9d technique. After the initial rf pulse is turned off, the magnetic moments of the nuclei begin to once again precess in phase around the constant magnetic field B0. However, the individual magnetic moments begin to diverge as some nuclei precess faster and some precess slower than the central Larmor frequency. When the magnetic moments are first tipped by the rf pulse, a relatively strong signal or voltage is induced in the receiver coils. However, the signal gradually decreases due to energy exchange between spins (with a spin-spin relaxation time constant T2) and the dephasing of the spins, both of which are cumulatively characterized by a relaxation time T2*. This signal is called the xe2x80x9cfree induction decayxe2x80x9d (FID).
A xe2x80x9cspin echoxe2x80x9d or subsequent representation of the FID can be generated by bringing the spins of the magnetic moments back into phase coherence by subjecting the sample to another rf pulse, called a xe2x80x9crefocusing pulse.xe2x80x9d For example, if, at a time xcfx84 after the nuclear spins are tipped by a first rf pulse of appropriate frequency, magnitude, and duration (a 90xc2x0 pulse), another electromagnetic signal of appropriate frequency, magnitude, and duration is applied to effect a 180xc2x0 nutation of the nuclear spins (a 180xc2x0 pulse), each individual spin is effectively rotated by 180xc2x0 (in the rotating frame of reference). As a result, the phase becomes the negative of the phase accumulated before the 180xc2x0 pulse in the former case. The magnetic moments that had been precessing faster than the central Larmor frequency, and thus xe2x80x9caheadxe2x80x9d of the other magnetic moments before the 180xc2x0 pulse, are now xe2x80x9cbehindxe2x80x9d the slower magnetic moments. As the faster magnetic moments xe2x80x9ccatch-upxe2x80x9d to the slower magnetic moments, a stronger and stronger signal is induced in the receiver coil until the faster magnetic moments pass the slower ones. The signal begins to fade as the magnetic moments spread out. In this manner, a so-called xe2x80x9cspin echoxe2x80x9d signal of the FID is generated. The peak amplitude of the spin echo depends upon the transverse or spin-spin relaxation time constant T2.
Ideally, the envelope of a spin-echo voltage signal is symmetrical in time. However, because of timing limitations between the initial rf excitation of the sample and the subsequent rf refocusing pulse, the initial portion of the spin-echo signal is generally not recoverable. Consequently, in practice, only a portion (e.g., half or slightly more than half) of the spin-echo signal can be used to obtain the associated NMR spectrum. The resulting spectrum is essentially a properly phased real component of the Fourier-transformed raw half spin-echo voltage signal. Since the imaginary part of the spectrum is more dispersive in terms of peak width, the NMR spectrum is often displayed in a real mode rather than the absolute value mode.
While this approach sometimes provides for an adequate spectrum, it is much preferred to have a spectrum with the highest possible signal to noise ratio (SNR) and spectral resolution, particularly for samples where the resonance peaks are closely spaced and the peak of tissue water needs to be suppressed. To date, NMR spectroscopists have had to use the half spin echo and accept the poor signal to noise ratio (SNR) and spectral resolution available from the half spin-echo signal.
Accordingly, there is need for a technique that could provide for high-resolution NMR spectra.
The present invention improves the quality of an NMR spectrum by acquiring more than half echo data and using an iterative numerical method to reconstruct the missing data points of the corresponding full symmetrical echo data.
A first aspect of the invention is a method of forming a high-resolution NMR spectrum. The method includes acquiring an initial partial spin-echo signal from a sample, the signal beginning at a time t=ti and having an echo-center portion. A low-resolution phase is then obtained from the echo-center portion, preferably by filtering the signal to isolate the echo-center and then Fourier-transforming the filtered signal. The partial spin-echo signal is then Fourier-transformed to obtain an initial spectrum having an initial phase. The phase of the initial spectrum is then replaced with the low-resolution phase to create a phase-constrained spectrum. The phase-constrained spectrum is then Fourier-transforming to obtain a reconstructed signal having data for time t less than ti. The data in the reconstructed signal for time t greater than ti is then replaced with that of the initial signal to form a modified reconstructed signal. This modified signal is then Fourier-transformed to obtain a new initial spectrum with a new initial phase. The acts from replacing the initial phase in the initial spectrum with the low-resolution phase to obtaining a reconstructed signal are iterated until the reconstructed remains substantially unchanged from the previous iteration. The reconstructed signal is then Fourier-transformed to obtain a high-resolution NMR spectrum.
A second aspect of the invention is an apparatus for obtaining a high-resolution NMR spectrum of a sample. The apparatus includes a magnet having an inner surface that defines an open volume and that creates a constant magnetic field within the open volume. Gradient coils are arranged adjacent the magnet inner surface. An rf coil is arranged adjacent the gradient coils opposite the magnet inner surface and adapted to be in electromagnetic communication with the sample. A receiving unit is electrically connected to the rf coil for receiving signals detected by the rf coil. A power supply is electrically connected to the gradient coils, for creating gradient magnetic fields within the open volume. A receiving unit is electrically connected to the rf coil. An analog-to-digital converter is electrically connected to the receiving unit and converts the analog signal from the rf coil to a digital partial spin-echo signal. A computer system is electrically connected to the analog-to-digital converter and receives the digital signal. The computer system includes a processor programmed to condition and iteratively process the digital signal so as to form a reconstructed spin-echo signal representative of the high-resolution NMR spectrum.
A third aspect of the invention is a computer-readable medium having computer-executable instructions to cause the computer system of the apparatus of the present invention to perform the method of the first aspect of the present invention, described briefly above.